Reactive robot navigation using optimal timing control

In this paper a solution is presented for the problem of avoiding obstacles while progressing towards a goal for a single robot. In particular, an optimal solution is obtained by allowing the robot to switch between a fixed number of behaviors and optimizing over what behaviors to use and when to switch between them. We moreover show that the structure of the switch law only depends on the distance between the obstacle and the goal. Hence, once initial simulations are done, the structure of the guard is known to the robot and, given that the robot knows the distance between the obstacle and the goal, it knows when to switch to obtain the optimal solution. Therefore the solution lends itself to real-time implementations. The feasibility of the approach is verified in real robotics experiments.